What is the derivative of (y^3c(x-c)^2) ?

The derivative of (y^3c(x-c)^2) is c(3y^2(dy)/(dx)(x-c)^2+2(x-c)y^3)

What is the first derivative of (y^3c(x-c)^2) ?

The first derivative of (y^3c(x-c)^2) is c(3y^2(dy)/(dx)(x-c)^2+2(x-c)y^3)

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Popular >

\frac{d}{d x} ((y^{3}) c (x - c)^{2})

c (3 y^{2} \frac{d y}{d x} (x - c)^{2} + 2 (x - c) y^{3})

Solution steps

\frac{d}{d x} ((y^{3}) c (x - c)^{2})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= c \frac{d}{d x} (y^{3} (x - c)^{2})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{3}, g = (x - c)^{2}

= c (\frac{d}{d x} (y^{3}) (x - c)^{2} + \frac{d}{d x} ((x - c)^{2}) y^{3})

\frac{d}{d x} (y^{3}) = 3 y^{2} \frac{d y}{d x}

\frac{d}{d x} ((x - c)^{2}) = 2 (x - c)

= c (3 y^{2} \frac{d y}{d x} (x - c)^{2} + 2 (x - c) y^{3})

(x^{2} - 2 x - 3)^{5}

(8 x - 20) \circ

\frac{4 x}{( 79 - x ) ( 21 - x )}

(2 a + 3) + 5 a

20 x^{21} x^{22} x^{23}

What is the derivative of (y^3c(x-c)^2) ?
The derivative of (y^3c(x-c)^2) is c(3y^2(dy)/(dx)(x-c)^2+2(x-c)y^3)
What is the first derivative of (y^3c(x-c)^2) ?
The first derivative of (y^3c(x-c)^2) is c(3y^2(dy)/(dx)(x-c)^2+2(x-c)y^3)